Csomos, Petra and Farkas, Balint and Kovacs, Balazs (2023) Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA JOURNAL OF NUMERICAL ANALYSIS, 43 (6). pp. 3628-3655. ISSN 0272-4979, 1464-3642
Full text not available from this repository. (Request a copy)Abstract
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | OVERCOMING ORDER REDUCTION; ALLEN-CAHN EQUATION; SEMIGROUPS; BULK; Lie splitting; error estimates; boundary coupling; semilinear problems |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Mar 2024 06:55 |
| Last Modified: | 20 Mar 2024 06:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/60130 |
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